In some available methods of producing a MOS transistor gate electrode (see, for instance, Japanese Unexamined Patent Publication (Kokai) No. 2006-86272), an electrically conductive material is embedded in a concave portion (hereinafter referred to as gate trench) formed in an insulating film. To produce MOS transistors with a finer structure, narrower gate trenches are needed in recent years, making it difficult to embed an electrically conductive material in them.